A058709 McKay-Thompson series of class 54a for Monster.

1, 0, 1, 1, 0, -1, 1, 0, 0, 2, 0, -1, 2, 0, 1, 3, 0, -1, 4, 0, 1, 5, 0, -1, 6, 0, 2, 7, 0, -1, 9, 0, 1, 11, 0, -2, 13, 0, 2, 16, 0, -2, 19, 0, 2, 23, 0, -3, 27, 0, 4, 32, 0, -3, 38, 0, 4, 44, 0, -5, 52, 0, 5, 61, 0, -6, 71, 0, 6, 82, 0, -7, 95, 0, 8, 110, 0, -8, 127, 0, 9, 145, 0, -9

Offset

-1,10

Links

G. C. Greubel, Table of n, a(n) for n = -1..2500

D. Ford, J. McKay and S. P. Norton, More on replicable functions, Comm. Algebra 22, No. 13, 5175-5193 (1994).

Index entries for McKay-Thompson series for Monster simple group

Formula

Expansion of A + q^2/A, where A = q*(eta(q^6)*eta(q^27)/(eta(q^3)* eta(q^54))), in powers of q. - G. C. Greubel, Jun 27 2018

Example

T54a = 1/q + q + q^2 - q^4 + q^5 + 2*q^8 - q^10 + 2*q^11 + q^13 + 3*q^14 - ...

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q]; A:= q*(eta[q^6]*eta[q^27]/(eta[q^3]* eta[q^54])); a:= CoefficientList[Series[A + q^2/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 27 2018 *)

Prog

(PARI) q='q+O('q^70); A = eta(q^6)*eta(q^27)/(eta(q^3)*eta(q^54)); Vec(A + q^2/A) \\ G. C. Greubel, Jun 27 2018

Crossrefs

Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.

Sequence in context: A105186 A328346 A238406 * A025842 A141100 A270655

Adjacent sequences: A058706 A058707 A058708 * A058710 A058711 A058712

Keyword

sign

Author

N. J. A. Sloane, Nov 27 2000

Extensions

Terms a(24) onward added by G. C. Greubel, Jun 27 2018

Status

approved